The present invention relates to an apparatus and method for controlling the behavior (repulsive or attractive) and magnitude of dispersion forces, such as the Casimir force.
Quantum field theory predicts, and experimentation has confirmed, that two, parallel, neutral (i.e., not electrically charged) planar slabs of any material that are separated from one another give rise to a mutually attractive force. This force is usually called the Casimir force after the theorist that postulated its existence in 1948.
The Casimir force is due to the perturbation, caused by the slab boundaries, on the random oscillations (due to Heisenberg""s uncertainty principle) of the electromagnetic field. In the region of space that is not between the slabs, the values of the electric and magnetic fields can freely fluctuate. But in the region of space that is between the slabs, the modes of oscillation of the electric and magnetic fields are restricted. Consequently, a gradient arises wherein the energy density in the region that is not between the slabs is greater than the energy density in the region between the slabs. This gradient is ultimately responsible for the Casimir force.
Most theoretical analyses have treated the Casimir force as an attractive force. But it has been suggested that, under certain circumstances, the Casimir force might manifest as a repulsive interaction. This is a consequence of the symmetry of the Maxwell equations under appropriate exchanges of the electric and magnetic fields. In particular, it has been predicted that the Casimir force between a perfectly conducting and a perfectly magnetically permeable material is repulsive. While this prediction has not been tested experimentally, it is based on the same body of evidence that has produced all the predictions about the Casimir force that have been verified to date.
In a recent treatment, the Casimir force is considered to be the net force that results from the contribution of each of an infinite number of spectral (i.e., frequency/wavelength) components. See Ford, L. H., xe2x80x9cSpectrum of the Casimir Effect and the Lifshitz Theory,xe2x80x9d Phys. Rev. A, vol. 48, no. 4, p 2962 (1993), incorporated by reference herein. By analyzing the oscillations that comprise the Casimir force on a frequency-by-frequency basis, the contribution of each frequency to the total Casimir force can be determined. According to this work, the Casimir force appears to be the net result of a xe2x80x9cnearxe2x80x9d exact cancellation of forces at all frequencies, all of which forces are much larger than the net force (i.e., the resulting Casimir force).
A question arises as to whether or not it is possible to controllably alter this infinite sum of terms. If it is possible, for example, to include only the xe2x80x9cattractivexe2x80x9d contributions or only the xe2x80x9crepulsivexe2x80x9d contributions, then the xe2x80x9csignxe2x80x9d or xe2x80x9cbehaviorxe2x80x9d (i.e., repulsive or attractive) of the Casimir force can be controllably determined. Furthermore, if the contributions can be manipulated in this manner, then, in principle at least, the magnitude of the force can be increased without limit. See, Ford, L. H., xe2x80x9cCasimir Force Between a Dielectric Sphere and a Wall: A Model for Amplification of Vacuum Fluctuations,xe2x80x9d Phys. Rev. A, vol. 58, no. 6, p. 4279 (1998), incorporated by reference herein.
Until now, no one has identified a system of two parallel plates that allows for the isolation of certain contributions while suppressing all others. This has been attributed to the fact that materials cannot be devised (due to fundamental physical reasons relating to causality) whose bulk properties display the necessary optical characteristics.
In accordance with the present teachings, the behavior and magnitude of a dispersion force is controllably altered by allowing the propagation of only those spectral components (i.e., frequencies) at which the random oscillations of the electromagnetic field contribute to the force behavior desired, while substantially suppressing all other spectral components.
In one embodiment, selective retention/suppression of spectral components is achieved by disposing two elements in spaced relation to one another. At least one of the elements comprises at least one periodic structure that is advantageously capable of achieving omni-directional selective reflection of selected spectral components. In some embodiments, such omni-directional selective reflection is obtained using photonic band gap material.
In embodiments in which the dispersion force is controllably altered to exhibit a repulsive force, the elements will repel each other. Consequently, in some embodiments wherein one of the elements is restrained from movement, the other element will xe2x80x9cfloatxe2x80x9d above it. The ability to control dispersion forces as described herein has many important applications in the areas of telecommunications, transportation, and propulsion, to name but a few.